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# Algorithm of exponentially weighted moving averages control chart for multivariate statistical control of process dispersion

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T.I. Svyatova – Post-graduate Student, Department «Applied Mathematics and Informatics», Ulyanovsk State Tech-nical University. E-mail: tatyana.krasko@rambler.ru V.N. Klyachkin – Dr. Sc. (Eng.), Professor, Department «Applied Mathematics and Informatics», Ulyanovsk State Technical University. E-mail: v_kl@mail.ru

The main tool of multivariate statistical process control is a Hotelling control chart, the purpose of which is monitoring changes in the average level of the process. There are several types of control chart to control multivariate process dispersion: generalized variance control chart, effective variance control chart and their modification. The efficiency of the process control is determined by the sensitivity of control charts to possible variations, particular, for increase of process dispersion. It has been shown that the sensitivity of generalized variance control chart is higher than sensitivity of effective variance control chart, but it is often insufficient to detect a small increase of the process dispersion. To increase the sensitivity of control charts is offered to use the algorithm of exponentially weighted moving averages control for the generalized variance. The algorithm includes two parameters that have to be estimated: the smoothing parameter and the parameter indicating the position of the control limits. The methods of estimates these parameters based on the results of statistical tests is offered. As an example, the data of monitoring the variance stability of the metallization thickness in the manufacture of printed circuit board were used. The proposed method of parameters estimation allows the use of considered algorithm to control a multivariate process dispersion.
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